The spirit of computer dating, lacking only the technology, was one of a number of schemes by which Charles Fourier wanted to radically transform human sexual relations. Early 19th century socialist thought, socialist movements and experiments were concerned with the entire catalog of miseries afflicting humankind. Monogamy and all its woes figured far more prominently than surplus value, which (according to pharmacists' records) was rarely the cause of suicidal depression. The Marxist tradition, while paying lip service to the “utopian” (...) critique of bourgeois society, repressed most of the “cultural” concerns of early socialism. The Utopians did not ignore or accept capitalism; it was a major evil, but not necessarily the source of all the other evils. (shrink)

The notion of an instrument in the quantum theory of measurement is studied in the context of transformation valued linear maps on von Neumann algebras and their *-subalgebras. An extension theorem is proved which yields among other things characterizations of the Fourier transforms of instruments and their noncommutative analogues. As an application, an ergodic type theorem for a general class of transformation valued functions on a locally compact group is obtained.

Albert Abraham Michelson (1852-1931), the American optical physicist best known for his precise determination of the velocity of light and for his experiments concerning aether drift, is less often acknowledged as the creator of new spectroscopic instrumentation and new spectroscopies. He devised a new method of light analysis relying upon his favourite instrument – a particular configuration of optical interferometer – and published investigations of spectral line separation, Doppler-broadening and simple high-resolution spectra (1887-1898). Contemporaries did not pursue his method. Michelson (...) himself discarded the technique by the end of the decade, promoting a new device, the ‘echelon spectroscope’, as a superior instrument. High-resolution spectroscopy was taken up by others at the turn of the century using the echelon, Fabry-Pérot etalon and similar instruments. Michelson’s ‘Light Wave Analysis’ was largely forgotten, but was rediscovered c1950 and developed over the following three decades into a technique rechristened ‘Fourier transform spectroscopy’. This paper presents Michelson’s interferometric work as a continuum of personal interests and historical context as an example of 'research technology' and 'peripheral science'. (shrink)

A formulation of quantum mechanics (QM) in the relativistic configurational space (RCS) is considered. A transformation connecting the non-relativistic QM and relativistic QM (RQM) has been found in an explicit form. This transformation is a direct generalization of the Kontorovich–Lebedev transformation. It is shown also that RCS gives an example of non-commutative geometry over the commutative algebra of functions.

The long-periodic/infinite discrete Gabor transform is more effective than the periodic/finite one in many applications. In this paper, a fast and effective approach is presented to efficiently compute the Gabor analysis window for arbitrary given synthesis window in DGT of long-periodic/infinite sequences, in which the new orthogonality constraint between analysis window and synthesis window in DGT for long-periodic/infinite sequences is derived and proved to be equivalent to the completeness condition of the long-periodic/infinite DGT. By using the property of delta function, (...) the original orthogonality can be expressed as a certain number of linear equation sets in both the critical sampling case and the oversampling case, which can be fast and efficiently calculated by fast discrete Fourier transform. The computational complexity of the proposed approach is analyzed and compared with that of the existing canonical algorithms. The numerical results indicate that the proposed approach is efficient and fast for computing Gabor analysis window in both the critical sampling case and the oversampling case in comparison to existing algorithms. (shrink)

Die vorliegende Auswahl von Texten des französischen Sozialphilosophen und Gesellschaftstheoretikers Charles Fourier (1772-1837) hat zwei Schwerpunkte: Zum einen thematisiert sie die wesentlichen Aspekte und die gedankliche Struktur von Fouriers weitreichendem Œuvre; zum anderen macht sie verständlich, welche Überlegungen Fouriers für heutige Theoretikerinnen und Theoretiker anregend oder anschlussfähig sind. Zu den Themen, die Fourier in den im vorliegenden Band publizierten Schriften behandelt, zählen das Ideal einer exakten Sozialwissenschaft; die Grundlagen der Anthropologie; die „neue Welt“ der Liebe und des Konsums; (...) die Relevanz der Arbeit für ein gelingendes Leben; die Grundstruktur nicht-entfremdeter Gesellschaften; sowie die Kritik an der Philosophie und den Gesellschaftswissenschaften, insbesondere der Ökonomik. Zahlreiche der im Band versammelten Texte werden erstmals auf Deutsch veröffentlicht. (shrink)

Objective: To evaluate feasibility of the guidelines of the Groupe Francophone de Réanimation et Urgence Pédiatriques for limitation of treatments in the paediatric intensive care unit .Design: A 2-year prospective survey.Setting: A 12-bed PICU at the Hôpital Jeanne de Flandre, Lille, France.Patients: Were included when limitation of treatments was expected.Results: Of 967 children admitted, 55 were included with a 2-day median delay. They were younger than others , had a higher paediatric risk of mortality score , and a higher paediatric (...) overall performance category score at admission ; all p<0.002. 34 children died. A limitation decision was made without meeting for 7 children who died: 6 received do-not-resuscitate orders and 1 received withholding decision. Decision-making meetings were organised for 31 children, and the following decisions were made: 12 DNROs , 4 withholding , with 14 withdrawing and 1 continuing treatment . After limitation, 21 children died and 10 survived . 13 procedures were interrupted because of death and 11 because of clinical improvement . Parents’ opinions were obtained after 4 family conferences , 3 days after inclusion. The first meeting was planned for 6 days after inclusion and held on the 7th day after inclusion; 80% of parents were immediately informed of the decision, which was implemented after half a day.Conclusions: GFRUPs procedure was applicable in most cases. The main difficulties were anticipating the correct date for the meeting and involving nurses in the procedure. Children for whom the procedure was interrupted because of clinical improvement and who survived in poor condition without a formal decision pointed out the need for medical criteria for questioning, which should systematically lead to a formal decision-making process. (shrink)

Using Type-2 theory of effectivity, we define computability notions on the spaces of Lebesgue-integrable functions on the real line that are based on two natural approaches to integrability from measure theory. We show that Fourier transform and convolution on these spaces are computable operators with respect to these representations. By means of the orthonormal basis of Hermite functions in L2, we show the existence of a linear complexity bound for the Fourier transform.

Using Type‐2 theory of effectivity, we define computability notions on the spaces of Lebesgue‐integrable functions on the real line that are based on two natural approaches to integrability from measure theory. We show that Fourier transform and convolution on these spaces are computable operators with respect to these representations. By means of the orthonormal basis of Hermite functions in L2, we show the existence of a linear complexity bound for the Fourier transform. (© 2004 WILEY‐VCH Verlag GmbH & (...) Co. KGaA, Weinheim). (shrink)

How might artificial neural networks (ANNs) inform cognitive science? Often cognitive scientists use ANNs but do not examine their internal structures. In this paper, we use ANNs to explore how cognition might represent musical properties. We train ANNs to classify musical chords, and we interpret network structure to determine what representations ANNs discover and use. We find connection weights between input units and hidden units can be described using Fourier phase spaces, a representation studied in musical set theory. We (...) find the total signal coming through these weighted connection weights is a measure of the similarity between two Fourier structures: the structure of the hidden unit's weights and the structure of the stimulus. This is surprising because neither of these Fourier structures is computed by the hidden unit. We then show how output units use such similarity measures to classify chords. However, we also find different types of units—units that use different activation functions—use this similarity measure very differently. This result, combined with other findings, indicates that while our networks are related to the Fourier analysis of musical sets, they do not perform Fourier analyses of the kind usually described in musical set theory. Our results show Fourier representations of music are not limited to musical set theory. Our results also suggest how cognitive psychologists might explore Fourier representations in musical cognition. Critically, such theoretical and empirical implications require researchers to understand how network structure converts stimuli into responses. (shrink)

Vesely (experimental physics, U. of Vienna, Austria) provides the basic numerical and computational techniques, followed by an explanation of specific problems of computational physics. Appendices address properties of computing machines and an outline of the technique of Fast Fourier Transformation. The first edition, published by Plenum Press, Ne.

We define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance ellipsoid of a quantum state on the configuration and momentum spaces form what we call a dual quantum pair. We thereafter show that quantum polarity allows solving the Pauli reconstruction problem for Gaussian wavefunctions. The notion of quantum polarity exhibits a (...) strong interplay between the uncertainty principle and symplectic and convex geometry and our approach could therefore pave the way for a geometric and topological version of quantum indeterminacy. We relate our results to the Blaschke–Santaló inequality and to the Mahler conjecture. We also discuss the Hardy uncertainty principle and the less-known Donoho–Stark principle from the point of view of quantum polarity. (shrink)

It is generally believed that the uncertainty relation Δq Δp≥1/2ħ, where Δq and Δp are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the path (...) of a particle in an interference experiment (such as the double-slit experiment).The failure of the uncertainty relation to produce these results is not a question of the interpretation of the formalism; it is a mathematical fact which follows from general considerations about the widths of wave functions.To express the uncertainty principle, one must distinguish two aspects of the spread of a wave function: its extent and its fine structure. We define the overall widthW Ψ and the mean peak width wψ of a general wave function ψ and show that the productW Ψ w φ is bounded from below if φ is the Fourier transform of ψ. It is shown that this relation expresses the uncertainty principle as it is used in the single- and double-slit experiments. (shrink)

We introduce a new Turing machine based concept of time complexity for functions on computable metric spaces. It generalizes the ordinary complexity of word functions and the complexity of real functions studied by Ko [19] et al. Although this definition of TIME as the maximum of a generally infinite family of numbers looks straightforward, at first glance, examples for which this maximum exists seem to be very rare. It is the main purpose of this paper to prove that, nevertheless, the (...) definition has a large number of important applications. Using the framework of TTE [40], we introduce computable metric spaces and computability on the compact subsets. We prove that every computable metric space has a c-proper c-admissible representation. We prove that Turing machine time complexity of a function computable relative to c-admissible c-proper representations has a computable bound on every computable compact subset. We prove that computably compact computable metric spaces have concise c-proper c-admissible representations and show by examples that many canonical representations are of this kind. Finally, we compare our definition with a similar one by Labhalla et al. [22]. Several examples illustrate the concepts. By these results natural and realistic definitions of computational complexity are now available for a variety of numerical problems such as image processing, integration, continuous Fourier transform or wave propagation. (shrink)

Experimental tests of various trace formulas, which in general relate the density of states for a given quantum mechanical system to the properties of the periodic orbits of its classical counterpart, for spectra of superconducting microwave billiards of varying chaoticity are reviewed by way of examples. For a two-dimensional Bunimovich stadium billiard the application of Gutzwiller's trace formula is shown to yield correctly locations and strengths of the peaks in the Fourier transformed quantum spectrum in terms of the shortest (...) unstable classical periodic orbits. Furthermore, in two-dimensional billiards of the Limaçon family the transition from regular to chaotic dynamics is studied in terms of a recently derived general trace formula by Ullmo, Grinberg and Tomsovic. Finally, some salient features of wave dynamical chaos in a fully chaotic three-dimensional Sinai microwave billiard are discussed. Here the reconstruction of the spectrum is not as straightforward as in the two-dimensional cases and a modified trace formula as suggested by Balian and Duplantier will have eventually to be applied. (shrink)

In the automatic detection of epileptic seizures, the monitoring of critically ill patients with time varying EEG signals is an essential procedure in intensive care units. There is an increasing interest in using EEG analysis to detect seizure, and in this study we aim to get a better understanding of how to visualize the information in the EEG time-frequency feature, and design and train a novel random forest algorithm for EEG decoding, especially for multiple-levels of illness. Here, we propose an (...) automatic detection framework for epileptic seizure based on multiple time-frequency analysis approaches; it involves a novel random forest model combined with grid search optimization. The short-time Fourier transformation visualizes seizure features after normalization. The dimensionality of features is reduced through principal component analysis before feeding them into the classification model. The training parameters are optimized using grid search optimization to improve detection performance and diagnostic accuracy by in the recognition of three different levels epileptic of conditions (healthy subjects, seizure-free intervals, seizure activity). Our proposed model was used to classify 500 samples of raw EEG data, and multiple cross-validations were adopted to boost the modeling accuracy. Experimental results were evaluated by an accuracy, a confusion matrix, a receiver operating characteristic curve and an area under the curve. The evaluations indicated that our model achieved the more effective classification than some previous typical methods. Such a scheme for computer-assisted clinical diagnosis of seizures has a potential guiding significance, which not only relieves the suffering of patient with epilepsy to improve quality of life, but also helps neurologists reduce their workload. (shrink)

The requirement of gauge invariance for the Schwinger-DeWitt equations, interpreted as a manifestly covariant quantum theory for the evolution of a system in spacetime, implies the existence of a five-dimensional pre-Maxwell field on the manifold of spacetime and “proper time” τ. The Maxwell theory is contained in this theory; integration of the field equations over τ restores the Maxwell equations with the usual interpretation of the sources. Following Schwinger's techniques, we study the Green's functions for the five-dimensional hyperbolic field equations (...) for both signatures ± [corresponding to O(4, 1) or O(3, 2) symmetry of the field equations] of the proper time derivative. The classification of the Green's functions follows that of the four-dimensional theory for “massive” fields, for which the “mass” squared may be positive or negative, respectively. The Green's functions for the five-dimensional field are then given by the Fourier transform over the “mass” parameter. We derive the Green's functions corresponding to the principal part ΔP and the homogeneous function Δ 1 ; all of the Green's functions can be expressed in terms of these, as for the usual field equations with definite mass. In the O(3, 2) case, the principal part function has support for x2⩾τ2, corresponding to spacelike propagation, as well as along the light cone x2=0 (for τ=0). There can be no transmission ofinformation in spacelike directions, with this propagator, since the Maxwell field, obtained by integration over τ, does not contain this component of the support. Measurements are characterized by such an integration. The spacelike field therefore can dynamically establish spacelike correlations. (shrink)

Sound symbolism refers to non‐arbitrary mappings between the sounds of words and their meanings and is often studied by pairing auditory pseudowords such as “maluma” and “takete” with rounded and pointed visual shapes, respectively. However, it is unclear what auditory properties of pseudowords contribute to their perception as rounded or pointed. Here, we compared perceptual ratings of the roundedness/pointedness of large sets of pseudowords and shapes to their acoustic and visual properties using a novel application of representational similarity analysis (RSA). (...) Representational dissimilarity matrices (RDMs) of the auditory and visual ratings of roundedness/pointedness were significantly correlated crossmodally. The auditory perceptual RDM correlated significantly with RDMs of spectral tilt, the temporal fast Fourier transform (FFT), and the speech envelope. Conventional correlational analyses showed that ratings of pseudowords transitioned from rounded to pointed as vocal roughness (as measured by the harmonics‐to‐noise ratio, pulse number, fraction of unvoiced frames, mean autocorrelation, shimmer, and jitter) increased. The visual perceptual RDM correlated significantly with RDMs of global indices of visual shape (the simple matching coefficient, image silhouette, image outlines, and Jaccard distance). Crossmodally, the RDMs of the auditory spectral parameters correlated weakly but significantly with those of the global indices of visual shape. Our work establishes the utility of RSA for analysis of large stimulus sets and offers novel insights into the stimulus parameters underlying sound symbolism, showing that sound‐to‐shape mapping is driven by acoustic properties of pseudowords and suggesting audiovisual cross‐modal correspondence as a basis for language users' sensitivity to this type of sound symbolism. (shrink)

Plastic waste is a significant environmental problem for almost all countries; therefore, protecting the environment from the problem is crucial. The most sensible solution to these problems is substituting the natural aggregates with substantial plastic waste in various building materials. This study aimed to optimise the mixed design ratio of cement brick containing plastic waste as aggregate replacement. Plastic cement brick mixtures were prepared by the incorporation of four different types of plastic waste such as polyethylene terephthalate (PET), high-density polyethylene, (...) low-density polyethylene and polypropylene into cement bricks with different cement contents (150, 300 and 450 g) and plastic replacement percentages (0, 3 and 6%). Compressive strength and water absorption of the plastic cement bricks were analysed using a statistical model through the response surface methodology. It revealed the optimum cement brick mixed design is C3-1% PET with the compressive strength of 27.50 MPa and water absorption of 1.16%. The optimised plastic cement brick also satisfied the general ASTM C62-17 requirements for building bricks despite the higher porosity observed by the scanning electron microscopy. The results from Fourier transform infrared spectroscopy analysis also showed that the addition of the plastic waste into cement brick was unlikely to modify the chemical compound within the cement brick mixtures. Thus, the proposed mathematical model can predict the required hardened properties of plastic cement bricks and could lead to greater utilisation of plastic waste in building materials. (shrink)

Uncertainty relations and complementarity of canonically conjugate position and momentum observables in quantum theory are discussed with respect to some general coupling properties of a function and its Fourier transform. The question of joint localization of a particle on bounded position and momentum value sets and the relevance of this question to the interpretation of position-momentum uncertainty relations is surveyed. In particular, it is argued that the Heisenberg interpretation of the uncertainty relations can consistently be carried through in a (...) natural extension of the usual Hilbert space frame of the quantum theory. (shrink)

Weak measurement devices resemble band pass filters: they strengthen average values in the state space or equivalently filter out some ‘frequencies’ from the conjugate Fourier transformed vector space. We thereby adjust a principle of classical communication theory for the use in quantum computation. We discuss some of the computational benefits and limitations of such an approach, including complexity analysis, some simple examples and a realistic not-so-weak approach.

The brain-computer interface of steady-state visual evoked potential is one of the fundamental ways of human-computer communication. The main challenge is that there may be a nonlinear relationship between different SSVEP in other states. For improving the performance of SSVEP BCI, a novel CNN algorithm model is proposed in this study. Based on the discrete Fourier transform to calculate the signal's power spectral density, we perform zero-padding in the signal's time domain to improve its performance on the PSD and (...) make it more refined. In this way, the frequency point interval in the PSD of the SSVEP is consistent with the minimum gap between the stimulation frequency. Combining the nonlinear transformation capabilities of CNN in deep learning, a zero-padding frequency domain convolutional neural network model is proposed. Extensive experiments based on the SSVEP dataset validate the effectiveness of our method. The study verifies that the proposed ZPFDCNN method can improve the effectiveness of the SSVEP-based high-speed BCI ITR. It has massive potential in the application of BCI. (shrink)

A detection task was performed using different pictographic representations of objects in order to test the hypothesis that high-level information (familiarity) may influence detection thresholds. The stimuli were five versions of forms: outline drawings of objects, silhouettes, and three fragmented versions of forms derived from the outlines. The stimuli varied on two parameters: their nameability (easily nameable, hardly nameable, and not nameable) as assessed by a naming task, and their energy content as assessed by a two-dimensional fast-Fourier transform. The (...) greatest amount of energy was observed for silhouettes, and the amount of energy contained in the vertical and horizontal spatial frequency components was equivalent for outlines and the three versions of fragmented forms. Luminance thresholds for the detection of the forms were measured by means of an adaptive method. The results show that thresholds were determined only by the energy content of the stimuli. High-level semantic or name information had no influence on the detectability of the visual signal. The results are discussed in terms of the visibility of spatial frequency components at detection threshold. (shrink)

Some arguments, based on the possible spontaneous violation of the cosmological principle (represented by the observed large-scale structures of galaxies), on the Cartan geometry of simple spinors, and on the Fock formulation of hydrogen atom wave equation in momentum space, are presented in favor of the hypothesis that space-time and momentum space should be both conformally compactified and should both originate from the two four-dimensional homogeneous spaces of the conformai group, both isomorphic (S 3 ×S 1)/Z 2 and correlated by (...) conformal inversion, but should not necessarily be identified with them. Within this framework, the possible common origin for the SO(4) symmetry underlying the geometrical structure of the Universe, of Kepler orbits, and of the H atom is discussed. One of the consequences of the proposed hypothesis could be that any quantum field theory should be naturally free from both infrared and ultraviolet divergences. But then physical spaces defined as those where physical phenomena may be best described through some set of fields, could be different from those homogeneous spaces. A simple, exactly soluble, toy model, valid for a two-dimensional spacetime, is presented where the conjectured conformally compactified homogeneous spaces are both isomorphic to (S 1 ×S 1)/Z 2,while the possible physical spaces could be two finite lattices which are dual since Fourier transforms, represented by finite, discrete, sums, may be well defined on them. (shrink)

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are reviewed and an emerging link between them is outlined. It is shown that these methods employ a wide range of important mathematical concepts like, e.g., Fourier transforms, Galois fields and rings, finite, and related projective geometries, and entanglement, to mention a few. Some applications of the theory to quantum information tasks are also mentioned.

Aiming at the problem of radar target recognition of High-Resolution Range Profile under low signal-to-noise ratio conditions, a recognition method based on the Constrained Naive Least-Squares Generative Adversarial Network, Short-time Fourier Transform, and Convolutional Neural Network is proposed. Combining the Least-Squares Generative Adversarial Network with the Wasserstein Generative Adversarial Network with Gradient Penalty, the CN-LSGAN is presented and applied to the HRRP denoise. The frequency domain and phase features of HRRP are gained by STFT in order to facilitate feature (...) learning and also match the input data format of the CNN. These experimental results show that the CN-LSGAN has better data augmentation performance and can effectively avoid the model collapse compared to the generative adversarial network and LSGAN. Also, the method has better recognition performance than the one-dimensional CNN method and the Long Short-Term Memory network method. (shrink)

Aims to show graduate students and researchers the vital benefits of integrating mathematics into their study and experience of the physical world. This book details numerous topics from the frontiers of modern physics and mathematics such as convergence, Green functions, complex analysis, Fourier series and Fourier transform, tensors, and others.

In Ref. 1 we have considered the finite-dimensional quantum mechanics. There the quantum mechanical space of states wasV=C r. It is known that the second quantization of this space is the space of square-summable functions of finite number of variables(L 2(Rr,dx)) (Segal isomorphism). Creation and annihilation operators were introduced in Ref. 1, and the former coincided with the usual position and momentum operators in the conventional quantum mechanics. In this paper we shall investigate the spectral properties of field operators. We (...) shall show that the isomorphism between the exponential ofV andL 2(Rr,dx) can be understood as the decomposition by generalized eigenvectors of field operators (“Fourier transform”). (shrink)

Adapting gross motor movement to match the tempo of auditory rhythmic stimulation is a complex skill with a long developmental trajectory. Drumming tasks have previously been employed with infants and young children to measure the emergence of rhythmic entrainment, and may provide a tool for identification of those with atypical rhythm perception and production. Here we describe a new protocol for measuring infant rhythmic movement that can be employed at scale. In the current study, 50 two-year-olds drummed along with the (...) audiovisual presentation of four steady rhythms, using videos of isochronous drumming at 400, 500, 600, and 700 ms IOI, and provided their spontaneous motor tempo by drumming in silence. Toddlers’ drumming is observed from video recordings made in participants’ own homes, obtained via the Lookit platform for online infant studies. We use OpenPose deep-learning model to generate wireframe estimates of hand and body location for each video. The vertical displacement of the hand was extracted, and the power and frequency of infants’ rhythmic entrainment quantified using Fast Fourier Transforms. We find evidence for age-appropriate tempo-flexibility in our sample. Our results demonstrate the feasibility of a fully digital approach to measuring rhythmic entrainment from within the participant’s home, from early in development. (shrink)

Within the last decade, several approaches using quaternion numbers to handle and model multiband images in a holistic manner were introduced. The quaternion Fourier transform can be efficiently used to model texture in multidimensional data such as color images. For practical application, multispectral satellite data appear as a primary source for measuring past trends and monitoring changes in forest carbon stocks. In this work, we propose a texture-color descriptor based on the quaternion Fourier transform to extract relevant information (...) from multiband satellite images. We propose a new multiband image texture model extraction, called FOTO++, in order to address biomass estimation issues. The first stage consists in removing noise from the multispectral data while preserving the edges of canopies. Afterward, color texture descriptors are extracted thanks to a discrete form of the quaternion Fourier transform, and finally the support vector regression method is used to deduce biomass estimation from texture indices. Our texture features are modeled using a vector composed with the radial spectrum coming from the amplitude of the quaternion Fourier transform. We conduct several experiments in order to study the sensitivity of our model to acquisition parameters. We also assess its performance both on synthetic images and on real multispectral images of Cameroonian forest. The results show that our model is more robust to acquisition parameters than the classical Fourier Texture Ordination model. Our scheme is also more accurate for aboveground biomass estimation. We stress that a similar methodology could be implemented using quaternion wavelets. These results highlight the potential of the quaternion-based approach to study multispectral satellite images. (shrink)

Although a few new results are presented, this is mainly a review article on the relationship between finite-dimensional quantum mechanics and finite groups. The main motivation for this discussion is the hidden subgroup problem of quantum computation theory. A unifying role is played by a mathematical structure that we call a Hilbert *-algebra. After reviewing material on unitary representations of finite groups we discuss a generalized quantum Fourier transform. We close with a presentation concerning position-momentum measurements in this framework.

The formalism of (±)-frequency parts , previously applied to solution of the D'Alembert equation in the case of the electromagnetic field, is applied to solution of the Klein-Gordon equation for the K-G field in the presence of sources. Retarded and advanced field operators are obtained as solutions, whose frequency parts satisfy a complex inhomogeneous K-G equation. Fourier transforms of these frequency parts are solutions of the central equation, which determines the time dependence of the destruction/creation operators of the field. (...) The retarded field operator is resolved into kinetic and dissipative components. Correspondingly, the energy/stress tensor is resolved into three components; the power/force density, into two—a kinetic and a dissipative component. As in the analogous electromagnetic case the dissipation theorem is derived according to which work done by the dissipative power/force is negative: energy/momentum is dissipated from the sources to the K-G field. Boson quantization conditions are satisfied by the kinetic component but not by the dissipative component of the retarded K-G field. (shrink)

It is shown that in every gauge the potential of the electromagnetic field in the presence of sources is resolved by an extension of the Helmholtz theorem into a solenoidal component and an irrotational component irrelevant for description of the field. Only irrotational components are affected by gauge transformations; in Coulomb gauge the irrotational component vanishes: the potential is solenoidal. The method of solution of the wave equation by use of positive- and negative-frequency parts is extended to solutions of (...) D'Alembert's equation, and applied to equations satisfied by the potential in Coulomb gauge and the electric and magnetic vectors. Fourier transforms of potentials specifying destruction/creation operators become time dependent in the presence of sources. Our central equation states this time dependence. Frequency parts of Maxwell's equations are obtained. When the retarded potential in Coulomb gauge is resolved into kinetic and dissipative components, the latter is shown to be in radiation gauge. Correspondingly, the energy/stress tensor is resolved into three components; the power/force density, into two: a kinetic and a dissipative component. Work done by the latter component is negative: energy and momentum are dissipated from matter to radiation. Boson quantization conditions are satisfied by the kinetic component of the retarded potential, but commutators of the dissipative component are determined by the current sources. The energy/stress tensor and Hamiltonian of the field in the presence of sources are derived from the classical Lagrangian density. The relation between the Hamiltonian and the energy is shown to agree with the time dependence of the destruction/creation operators in Heisenberg picture. (shrink)

This study examines the hydrolysis of lignocellulose extracted from poultry manure for the purpose of investigating low-cost feedstocks for ethanol production while providing an alternative solid waste management strategy for agricultural livestock manures. Poultry manure underwent various pretreatments to enhance subsequent enzymatic hydrolysis including untreated, alkaline pretreatment with 0.5N KOH, drying, and grinding. The KOH-treated, dried, and grinded poultry manure yielded the highest glucose conversions. When poultry manure without pretreatment was hydrolyzed at 40°C with an enzyme loading 400 units/g feedstock, (...) 7.1 ± 0.3% was converted to glucose in 24 hours. This increased to 27.6 ± 1.2% when a KOH pretreatment followed by drying and grinding was applied. Fourier transform infrared spectroscopy analyses were used to examine differences in the composition of the pretreated feedstock before and after enzymatic hydrolysis. These indicate that the cellulose content in pretreated poultry manure was removed during enzymatic hydrolysis. (shrink)

Ancient algorithms -- Sorting -- Graph algorithms -- Primality testing -- Solution of linear equations -- Newton's method -- Linear programming -- Eigenvalues and eigenvectors -- MM algorithms -- Data mining -- The fast Fourier transform -- Monte Carlo methods -- Mathematical review.

The structure of rhodopsin is a subject of intense interest. Solving the structure by traditional methods has proved exceedingly challenging. It may therefore be useful to confront the problem by a combination of alternate techniques. These include FTIR (Fourier transform infrared spectroscopy) and AFM (atomic force microscopy) on the intact protein. Furthermore, additional insights may be gained through structural investigations of discrete rhodopsin domains.